A polynomial graph cuts the x-axis at (−4, 0), (1, 0), and (6, 0). How many real zeroes does it have?
Answer and explanation
Correct answer: Three
The geometrical rule for polynomial zeroes is that every point (r, 0) on the graph corresponds to p(r) = 0, so r is a real zero. The three listed points have different x-coordinates: −4, 1, and 6. Thus they represent three distinct real zeroes. The y-coordinate is 0 in each case because all three points lie on the x-axis. Option A counts only one point, Option B misses one of the three intersections, and Option D adds an unsupported fourth zero. The degree of the polynomial is not needed to answer the question; simply counting the distinct x-axis intersections gives three. Hence Option C is correct.
Frequently asked questions
What is the correct answer to this question?
Three
Why is this the correct answer?
The geometrical rule for polynomial zeroes is that every point (r, 0) on the graph corresponds to p(r) = 0, so r is a real zero. The three listed points have different x-coordinates: −4, 1, and 6. Thus they represent three distinct real zeroes. The y-coordinate is 0 in each case because all three points lie on the x-axis. Option A counts only one point, Option B misses one of the three intersections, and Option D adds an unsupported fourth zero. The degree of the polynomial is not needed to answer the question; simply counting the distinct x-axis intersections gives three. Hence Option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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